Question

Loki、Moe、Nick 和 Ott 是好朋友。Ott 没有钱，但其他人有钱。Moe 给了 Ott 自己钱数的五分之一，Loki 给了 Ott 自己钱数的四分之一，Nick 给了 Ott 自己钱数的三分之一。每个人给 Ott 的钱数相同。现在 Ott 拥有这群人总钱数的几分之几？

Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?

$\dfrac{1}{10}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{2}{5}$

$\dfrac{1}{2}$

答案：B

知识点：分数逆推法

难度评级：1560

解答：

不失一般性，假设每个人都给 Ott $\$1$ 。这意味着 Moe 原来有 $\$5$ ，Loki 原来有 $\$4$ ，Nick 原来有 $\$3$ 。

Ott 现在有 $\$3$ ，总钱数为 $\$5 + \$4 + \$3 = \$12.$

因此 Ott 拥有这群人总钱数的 $\dfrac{3}{12} = \dfrac{1}{4}$ ，也就是四分之一。

所以正确答案是 B。

WLOG, assume that everyone gave Ott $\$1.$ This means that Moe had $\$5,$ Loki had $\$4,$ and Nick had $\$3$ originally.

Ott now has $\$3,$ and the total amount of money is $\$5 + \$4 + \$3 = \$12.$

This means that Ott has $\dfrac{3}{12} = \dfrac{1}{4}$ of the group's money.

Thus, B is the correct answer.

2002 AMC 8 第 25 题

答案：B

难度评级：1560

解答：

其他年份的第 25 题